What is the name of the book which is a part of Ain-i-Akbari and gives a fascinating, detailed, and highly complex view of agrarian society in northern India? 

mulk-abadi 

The correct answer is Option 2 - mulk-abadi

The mulk-abadi gives a fascinating, detailed and highly complex view of agrarian society in northern India.

The "Ain-i-Akbari" is a part of the Akbarnama, and it is made up of five books (daftars), of which the first three books describe the administration. The first book, called manzil-abadi, concerns the imperial household and its maintenance. The second book, sipah-abadi, covers the military and civil administration and the establishment of servants. The third book, mulk-abadi, is the one which deals with the fiscal side of the empire and provides rich quantitative information on revenue rates.

After setting out details at the suba level, the Ain goes on to give a detailed picture of the sarkars below the suba. This it does in the form of tables, which have eight columns giving the following information: (1) parganat/mahal; (2) qila (forts); (3) arazi and zamin-i paimuda (measured area); (4) naqdi, revenue assessed in cash; (5) suyurghal, grants of revenue in charity; (6) zamindars; columns 7 and 8 contain details of the castes of these zamindars, and their troops including their horsemen (sawar), foot-soldiers (piyada) and elephants (fil). The mulk-abadi gives a fascinating, detailed and highly complex view of agrarian society in northern India. The fourth and fifth books (daftars) deal with the religious, literary and cultural traditions of the people of India and also contain a collection of Akbar’s “auspicious sayings”